Chapter 2: Q41E (page 77)
Find the vertical asymptotes of the function
\(f\left( x \right) = \frac{{x - {\bf{1}}}}{{{\bf{2}}x + {\bf{4}}}}\)
The vertical asymptote of the function is \(x = - 2\).
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
A particle moves along a straight line with the equation of motion\(s = f\left( t \right)\), where s is measured in meters and t in seconds.Find the velocity and speed when\(t = {\bf{4}}\).
\(f\left( t \right) = {\bf{80}}t - {\bf{6}}{t^{\bf{2}}}\)
For what value of the constant c is the function f continuous on \(\left( { - \infty ,\infty } \right)\)?
47. \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{c{x^{\bf{2}}} + {\bf{2}}x}&{{\bf{if}}\,\,\,x < {\bf{2}}}\\{{x^3} - cx}&{{\bf{if}}\,\,\,x \ge {\bf{2}}}\end{array}} \right.\)
(a)Where does the normal line to the ellipse\({x^2} - xy + {y^2} = 3\) at the point \((1, - 1)\)intersect the ellipse a second time?
(b)Illustrate part (a) by graphing the ellipse and the normal line.
41-42 Show that f is continuous on \(\left( { - \infty ,\infty } \right)\).
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{{\bf{sin}}\,x}&{{\bf{if}}\,\,x < \frac{\pi }{{\bf{4}}}}\\{{\bf{cos}}\,x}&{{\bf{if}}\,\,\,x \ge \frac{\pi }{{\bf{4}}}}\end{array}} \right.\)
The cost (in dollars) of producing \[x\] units of a certain commodity is \(C\left( x \right) = 5000 + 10x + 0.05{x^2}\).
(a) Find the average rate of change of \(C\) with respect to \[x\]when the production level is changed
(i) From \(x = 100\)to \(x = 105\)
(ii) From \(x = 100\)to \(x = 101\)
(b) Find the instantaneous rate of change of \(C\) with respect to\(x\) when \(x = 100\). (This is called the marginal cost. Its significance will be explained in Section 3.7.)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
